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Thread: Find the general solution of 4cosec (2x + 1) = 9

  1. June 13th 2006, 07:27 PM #1
    Kiwigirl
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    Question Find the general solution of 4cosec (2x + 1) = 9

    Find the general solution of the following trigonometric equation:

    4cosec (2x + 1) = 9
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  2. June 13th 2006, 08:31 PM #2
    Soroban
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    Hello, Kiwigirl!

    Find the general solution of: 4\csc(2x + 1) \;= \;9
    Divide by 4: . \csc(2x + 1) \;= \;\frac{9}{4}

    Take reciprocals: . \sin(2x + 1) \;= \;\frac{4}{9}

    Then: . 2x + 1 \;= \;\arcsin\left(\frac{4}{9}\right) + 2\pi n

    . . . 2x \;= \;\arcsin\left(\frac{4}{9}\right) + 2\pi n - 1

    . . . x \;= \;\frac{1}{2}\arcsin\left(\frac{4}{9}\right) + \pi n - \frac{1}{2}
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